Title : A quasi-complete homogeneous variety associated to a cubic form

Abstract :

To each non-degenerate cubic form, we associate a quasi-complete homogeneous variety. This homogeneous variety is rationally connected and can be realized as a projective co-adjoint orbit of a certain Lie algebra. We will study when  this homogeneous variety  has a smooth compactification with boundary of codimension at least 2. This is a joint work with Laurent Manivel.